The equation \( 15 x^{2}-1 x-2=0 \) has solutions of the form \[ x=\frac{N \pm \sqrt{D}}{M} \] (A) Use the quadratic formula to solve this equation and find the appropriate integer values of \( N, M \), and \( D \). Do not worry about simplifying the \( \sqrt{D} \) yet in this part of the problem. \[ N=\square ; D=\square \] s=

Solve the equation \( 15x^{2}-1x-2=0 \). Solve the quadratic equation by following steps: - step0: Solve by factoring: \(15x^{2}-1\times x-2=0\) - step1: Multiply the terms: \(15x^{2}-x-2=0\) - step2: Factor the expression: \(\left(3x+1\right)\left(5x-2\right)=0\) - step3: Separate into possible cases: \(\begin{align}&5x-2=0\\&3x+1=0\end{align}\) - step4: Solve the equation: \(\begin{align}&x=\frac{2}{5}\\&x=-\frac{1}{3}\end{align}\) - step5: Rewrite: \(x_{1}=-\frac{1}{3},x_{2}=\frac{2}{5}\) The solutions to the equation \(15x^{2}-1x-2=0\) are \(x_{1}=-\frac{1}{3}\) and \(x_{2}=\frac{2}{5}\). To find the appropriate integer values of \(N\), \(M\), and \(D\) using the quadratic formula, we can compare the solutions obtained with the general form of the quadratic formula: \[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this case, \(a = 15\), \(b = -1\), and \(c = -2\). Substituting these values into the quadratic formula, we get: \[ x = \frac{-(-1) \pm \sqrt{(-1)^2 - 4(15)(-2)}}{2(15)} \] \[ x = \frac{1 \pm \sqrt{1 + 120}}{30} \] \[ x = \frac{1 \pm \sqrt{121}}{30} \] \[ x = \frac{1 \pm 11}{30} \] Therefore, the appropriate integer values are: - \(N = 1\) - \(M = 30\) - \(D = 121\)